An EFB could be not used for this purpose and what it could do is would be replicated by the EICAS (engine indication and crew alert system). The reason for this is that your receiving, pre-flight and before takeoff checklists all involve physically moving switches. The EFB would be unable to perform these actions (e.g. an EFB cannot select flaps 9 degrees).
What an EFB could do, if tied into the aircrafts ARINC data bus, is to verify things. Such an EFB could verify that flaps are indicating a set position and could alert us if it were not. However, the EICAS already does this, and if I were to advance a thrust lever beyond taxi power I would get a master warning and a takeoff configuration EICAS message as well as an aural warning "TAKEOFF FLAPS" (EMB-145).
You also mention the bulk of paper carried as a reason for this, but this is not relevant to the checklists. The checklist on many large airplanes is a single sheet of paper, laminated and installed in the airplane. Some airplanes may have a few sheets, but overall checklists account for very little paperwork and they belong to the airplane, not the pilots.
Where EFBs do help with paperwork are the approach charts, which account for 75% of what I carried on any given flight. Three 2" binders, full of nothing but approach plates. An EFB can condense that down to a tablet, and this is where the value of the EFB is.